Mixed-Curvature Manifolds Interaction Learning for Knowledge Graph-aware Recommendation

As auxiliary collaborative signals, the entity connectivity and relation semanticity beneath knowledge graph (KG) triples can alleviate the data sparsity and cold-start issues of recommendation tasks. Thus many works consider obtaining user and item representations via information aggregation on graph-structured data within Euclidean space. However, the scale-free graphs (e.g., KGs) inherently exhibit non-Euclidean geometric topologies, such as tree-like and circle-like structures. The existing recommendation models built in a single type of embedding space do not have enough capacity to embrace various geometric patterns, consequently, resulting in suboptimal performance. To address this limitation, we propose a KG-aware recommendation model with mixed-curvature manifolds interaction learning, namely CurvRec. On the one hand, it aims to preserve various global geometric structures in KG with mixed-curvature manifold spaces as the backbone. On the other hand, we integrate Ricci curvature into graph convolutional networks (GCNs) to capture local geometric structural properties when aggregating neighbor nodes. Besides, to exploit the expressive spatial features in KG, we incorporate interaction learning to ensure the geometric message passing between curved manifolds. Specifically, we adopt curvature-aware geodesic distance metrics to maximize the mutual information between Euclidean space and non-Euclidean spaces. Through extensive experiments, we demonstrate that the proposed CurvRec outperforms state-of-the-art baselines.